Physics 145 Final Exam Reference Sheet: Core Equations and Concepts

Kinematics and Motion

Quadratic Formula and Projectile Motion

The quadratic formula is used to solve equations of the form ax2 + bx + c = 0:

• Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Projectile Motion: The motion of an object thrown or projected into the air, subject only to acceleration due to gravity.

Kinematic Equations for Constant Acceleration

These equations describe the motion of objects under constant acceleration:

• $v = v_0 + at$

• $x = x_0 + v_0 t + \frac{1}{2} a t^2$

• $v^2 = v_0^2 + 2a(x - x_0)$

• $x = x_0 + \frac{1}{2}(v_0 + v)t$

Horizontal Range of Projectile

• $R = \frac{v_0^2 \sin 2\theta}{g}$

Translational Equilibrium

• Condition: $\sum F = 0$

Uniform Circular Motion

• Relative Motion: $v_{rel} = v_{A/B} + v_{B/C}$

• Centripetal Acceleration: $a_c = \frac{v^2}{r}$

• Centripetal Force: $F_c = m a_c = m \frac{v^2}{r}$

Forces and Newton's Laws

Newton's Law of Gravitation

• $F_g = G \frac{m_1 m_2}{r^2}$, where $G = 6.67 \times 10^{-11} \text{N} \cdot \text{m}^2 / \text{kg}^2$

Force of Gravity Near Earth's Surface

• $F_g = mg$

Work, Energy, and Power

Work and Power

• $W = Fd \cos \theta$

• $P = \frac{W}{t}$

• $P = Fv$

Kinetic and Potential Energy

• $K = \frac{1}{2}mv^2$

• $U = mgh$

• Conservation of Energy: $E = K + U$

Momentum and Impulse

• $p = mv$

• $J = F \Delta t$

• Conservation of Momentum: $p_{initial} = p_{final}$

Rotational Motion

Angular Kinematics

• $\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2$

• $\omega = \omega_0 + \alpha t$

• $\omega^2 = \omega_0^2 + 2\alpha(\theta - \theta_0)$

Rotational Dynamics

• $\tau = I \alpha$

• $I = \sum m r^2$

• $K_{rotational} = \frac{1}{2} I \omega^2$

Equilibrium and Elasticity

Conditions for Equilibrium

• $\sum F = 0$

• $\sum \tau = 0$

Fluid Mechanics

Density and Pressure

• $\rho = \frac{m}{V}$

• $P = \frac{F}{A}$

Buoyant Force

• $F_B = \rho_{fluid} V_{sub} g$

Gravitation

• $F_g = G \frac{m_1 m_2}{r^2}$

Periodic Motion

Simple Harmonic Motion

• $x = A \cos(\omega t + \phi)$

• $T = 2\pi \sqrt{\frac{m}{k}}$

• $T = 2\pi \sqrt{\frac{l}{g}}$ (pendulum)

Thermodynamics

Temperature and Heat

• $\Delta L = \alpha L_0 \Delta T$

• $\Delta V = \beta V_0 \Delta T$

• $Q = mc \Delta T$

Ideal Gas Law

• $PV = nRT$

• $k_B = 1.38 \times 10^{-23} \text{J/K}$

• $N_A = 6.02 \times 10^{23}$

First Law of Thermodynamics

• $\Delta U = Q - W$

Additional info:

• This reference sheet covers essential formulas and concepts from introductory college physics, including kinematics, dynamics, energy, momentum, rotation, fluids, gravitation, periodic motion, and thermodynamics.

• Equations are presented in LaTeX format for clarity and academic rigor.